Relevant bibliographies by topics / Almgren's function

Academic literature on the topic 'Almgren's function'

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Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Almgren's function"

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De Lellis, Camillo, Matteo Focardi, and Emanuele Nunzio Spadaro. "Lower semicontinuous functionals for Almgren's multiple valued functions." Annales Academiae Scientiarum Fennicae Mathematica 36 (August 2011): 393–410. http://dx.doi.org/10.5186/aasfm.2011.3626.

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Logaritsch, Philippe, and Andrea Marchese. "Kirszbraun’s extension theorem fails for Almgren’s multiple valued functions." Archiv der Mathematik 102, no. 5 (May 2014): 455–58. http://dx.doi.org/10.1007/s00013-014-0642-4.

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Brendle, Simon, and Otis Chodosh. "On the Maximum Curvature of Closed Curves in Negatively Curved Manifolds." Canadian Mathematical Bulletin 58, no. 4 (December 1, 2015): 713–22. http://dx.doi.org/10.4153/cmb-2015-030-3.

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AbstractMotivated by Almgren’s work on the isoperimetric inequality, we prove a sharp inequality relating the length and maximum curvature of a closed curve in a complete, simply connected manifold of sectional curvature at most −1. Moreover, if equality holds, then the norm of the geodesic curvature is constant and the torsion vanishes. The proof involves an application of the maximum principle to a function defined on pairs of points.
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LØKKA, ARNE, and JUNWEI XU. "OPTIMAL LIQUIDATION TRAJECTORIES FOR THE ALMGREN–CHRISS MODEL." International Journal of Theoretical and Applied Finance 23, no. 07 (November 2020): 2050049. http://dx.doi.org/10.1142/s0219024920500491.

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We consider an optimal liquidation problem with infinite horizon in the Almgren–Chriss framework, where the unaffected asset price follows a Lévy process. The temporary price impact is described by a general function that satisfies some reasonable conditions. We consider a market agent with constant absolute risk aversion, who wants to maximize the expected utility of the cash received from the sale of the agent’s assets, and show that this problem can be reduced to a deterministic optimization problem that we are able to solve explicitly. In order to compare our results with exponential Lévy models, which provide a very good statistical fit with observed asset price data for short time horizons, we derive the (linear) Lévy process approximation of such models. In particular we derive expressions for the Lévy process approximation of the exponential variance–gamma Lévy process, and study properties of the corresponding optimal liquidation strategy. We then provide a comparison of the liquidation trajectories for reasonable parameters between the Lévy process model and the classical Almgren–Chriss model. In particular, we obtain an explicit expression for the connection between the temporary impact function for the Lévy model and the temporary impact function for the Brownian motion model (the classical Almgren–Chriss model), for which the optimal liquidation trajectories for the two models coincide.
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LIU, HAIRONG, FANG LIU, and HUI WU. "THE UNIQUE CONTINUATION PROPERTY OF -HARMONIC FUNCTIONS ON THE HEISENBERG GROUP." Bulletin of the Australian Mathematical Society 99, no. 2 (November 12, 2018): 219–30. http://dx.doi.org/10.1017/s0004972718001016.

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We introduce an Almgren frequency function of the sub-$p$-Laplace equation on the Heisenberg group to establish a doubling estimate under the assumption that the frequency function is locally bounded. From this, we obtain some partial results on unique continuation for the sub-$p$-Laplace equation.
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Garofalo, Nicola, and Kevin Rotz. "Properties of a frequency of Almgren type for harmonic functions in Carnot groups." Calculus of Variations and Partial Differential Equations 54, no. 2 (April 23, 2015): 2197–238. http://dx.doi.org/10.1007/s00526-015-0862-x.

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Luo, Haijun, and Zhitao Zhang. "Limit Configurations of Schrödinger Systems Versus Optimal Partition for the Principal Eigenvalue of Elliptic Systems." Advanced Nonlinear Studies 19, no. 4 (November 1, 2019): 693–715. http://dx.doi.org/10.1515/ans-2019-2057.

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AbstractWe study a Schrödinger system of four equations with linear coupling functions and nonlinear couplings, including the case that the corresponding elliptic operators are indefinite. For any given nonlinear coupling {\beta>0}, we first use minimizing sequences on a normalized set to obtain a minimizer, which implies the existence of positive solutions for some linear coupling constants {\mu_{\beta},\nu_{\beta}} by Lagrange multiplier rules. Then, as {\beta\to\infty}, we prove that the limit configurations to the competing system are segregated in two groups, develop a variant of Almgren’s monotonicity formula to reveal the Lipschitz continuity of the limit profiles and establish a kind of local Pohozaev identity to obtain the extremality conditions. Finally, we study the relation between the limit profiles and the optimal partition for principal eigenvalue of the elliptic system and obtain an optimal partition for principal eigenvalues of elliptic systems.
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BARGER, WESTON, and MATTHEW LORIG. "OPTIMAL LIQUIDATION UNDER STOCHASTIC PRICE IMPACT." International Journal of Theoretical and Applied Finance 22, no. 02 (March 2019): 1850059. http://dx.doi.org/10.1142/s0219024918500590.

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We assume a continuous-time price impact model similar to that of Almgren–Chriss but with the added assumption that the price impact parameters are stochastic processes modeled as correlated scalar Markov diffusions. In this setting, we develop trading strategies for a trader who desires to liquidate his inventory but faces price impact as a result of his trading. For a fixed trading horizon, we perform coefficient expansion on the Hamilton–Jacobi–Bellman (HJB) equation associated with the trader’s value function. The coefficient expansion yields a sequence of partial differential equations that we solve to give closed-form approximations to the value function and optimal liquidation strategy. We examine some special cases of the optimal liquidation problem and give financial interpretations of the approximate liquidation strategies in these cases. Finally, we provide numerical examples to demonstrate the effectiveness of the approximations.
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Arkæologisk Selskab, Jysk. "Anmeldelser 2012." Kuml 61, no. 61 (October 31, 2012): 259–317. http://dx.doi.org/10.7146/kuml.v61i61.24497.

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Holck Colding, Tobias, and William P. Minicozzi II. "Parabolic Frequency on Manifolds." International Mathematics Research Notices, April 19, 2021. http://dx.doi.org/10.1093/imrn/rnab052.

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Abstract We prove monotonicity of a parabolic frequency on static and evolving manifolds without any curvature or other assumptions. These are parabolic analogs of Almgren’s frequency function. When the static manifold is Euclidean space and the drift operator is the Ornstein–Uhlenbeck operator, this can been seen to imply Poon’s frequency monotonicity for the ordinary heat equation. When the manifold is self-similarly evolving by the Ricci flow, we prove a parabolic frequency monotonicity for solutions of the heat equation. For the self-similarly evolving Gaussian soliton, this gives directly Poon’s monotonicity. Monotonicity of frequency is a parabolic analog of the 19th century Hadamard three-circle theorem about log convexity of holomorphic functions on C. From the monotonicity, we get parabolic unique continuation and backward uniqueness.
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Dissertations / Theses on the topic "Almgren's function"

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NYS, MANON. "Schrödinger equations with an external magnetic field: spectral problems & semiclassical states." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2015. http://hdl.handle.net/10281/89252.

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In this thesis, we study Schrödinger equations with an external magnetic field. In the first part, we are interested in an eigenvalue problem. We work in an open, bounded and simply connected domain in dimension two. We consider a magnetic potential singular at one point in the domain, and related to the magnetic field being a multiple of a Dirac delta. Those two objects are related to the Bohm-Aharonov effect, in which a charged particle is influenced by the presence of the magnetic potential although it remains in a region where the magnetic field is zero. We consider the Schrödinger magnetic operator appearing in the Schrödinger equation in presence of an external magnetic field. We want to study the spectrum of this operator, and more particularly how it varies when the singular point moves in the domain. We prove some results of continuity and differentiability of the eigenvalues when the singular point moves in the domain or approaches its boundary. Finally, in case of half-integer circulation of the magnetic potential, we study some asymptotic behaviour of the eigenvalues close to their critical points. In the second part, we study nonlinear Schrödinger equations in a cylindrically setting. We are interested in the semiclassical limit of the equation. We prove the existence of a semiclassical solution concentrating on a circle. Moreover, the radius of that circle is determined by the electric potential, but also by the magnetic potential. This result is totally new with respect to the ones before, in which the concentration is driven only by the electric potential.
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Nys, Manon. "Schrödinger equations with an external magnetic field: Spectral problems and semiclassical states." Doctoral thesis, Universite Libre de Bruxelles, 2015. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/216641.

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In this thesis, we study Schrödinger equations with an external magnetic field. In the first part, we are interested in an eigenvalue problem. We work in an open, bounded and simply connected domain in dimension two. We consider a magnetic potential singular at one point in the domain, and related to the magnetic field being a multiple of a Dirac delta. Those two objects are related to the Bohm-Aharonov effect, in which a charged particle is influenced by the presence of the magnetic potential although it remains in a region where the magnetic field is zero. We consider the Schrödinger magnetic operator appearing in the Schrödinger equation in presence of an external magnetic field. We want to study the spectrum of this operator, and more particularly how it varies when the singular point moves in the domain. We prove some results of continuity and differentiability of the eigenvalues when the singular point moves in the domain or approaches its boundary. Finally, in case of half-integer circulation of the magnetic potential, we study some asymptotic behaviour of the eigenvalues close to their critical points. In the second part, we study nonlinear Schrödinger equations in a cylindrically setting. We are interested in the semiclassical limit of the equation. We prove the existence of a semiclassical solution concentrating on a circle. Moreover, the radius of that circle is determined by the electric potential, but also by the magnetic potential. This result is totally new with respect to the ones before, in which the concentration is driven only by the electric potential.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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"Multiple-valued functions in the sense of F. J. Almgren." Université catholique de Louvain, 2008. http://edoc.bib.ucl.ac.be:81/ETD-db/collection/available/BelnUcetd-05312008-222245/.

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Books on the topic "Almgren's function"

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(Editor), Vladimir Scheffer, and Jean E. Taylor (Editor), eds. Almgren's Big Regularity Paper: Q-Valued Functions Minimizing Dirichlet's Integral and the Regularity of Area-Minimizing Rectifiable Currents Up to Codimension ... Scientific Monograph Series in Mathematics). World Scientific Publishing Company, 2000.

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Book chapters on the topic "Almgren's function"

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"Approximation in Mass of a Nearly Flat Rectifiable Current Which Is Mass Minimizing in a Manifold by the Image of a Lipschitz Q(Rm+n) Valued Function Defined on a Center Manifold." In Almgren's Big Regularity Paper, 331–682. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812813299_0006.

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"Basic Properties of Q and Q Valued Functions." In Almgren's Big Regularity Paper, 34–90. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812813299_0003.

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"Bounds on the Frequency Functions and the Main Interior Regularity Theorem." In Almgren's Big Regularity Paper, 683–836. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812813299_0007.

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"Properties of Dir Minimizing Q Valued Functions and Tangent Cone Stratification of Mass Minimizing Rectifiable Currents." In Almgren's Big Regularity Paper, 91–224. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812813299_0004.

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"Approximation in Mass of Nearly Flat Rectifiable Currents Which Are Mass Minimizing in Manifolds by Graphs of Lipschitz Q Valued Functions Which Can Be Weakly Nearly Dir Minimizing." In Almgren's Big Regularity Paper, 225–330. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812813299_0005.

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Conference papers on the topic "Almgren's function"

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De Lellis, Camillo. "Almgren's Q-valued Functions Revisited." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0128.

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